Entity resolution (ER) is the problem of identifying and linking database records that refer to the same real-world entity. Traditional ER methods use batch processing, which becomes impractical with growing data volumes due to high computational costs and lack of real-time capabilities. In many applications, users need to resolve entities for only a small portion of their data, making full data processing unnecessary -- a scenario known as "ER-on-demand". This paper proposes FastER, an efficient ER-on-demand framework for property graphs. Our approach uses graph differential dependencies (GDDs) as a knowledge encoding language to design effective filtering mechanisms that leverage both structural and attribute semantics of graphs. We construct a blocking graph from filtered subgraphs to reduce the number of candidate entity pairs requiring comparison. Additionally, FastER incorporates Progressive Profile Scheduling (PPS), allowing the system to incrementally produce results throughout the resolution process. Extensive evaluations on multiple benchmark datasets demonstrate that FastER significantly outperforms state-of-the-art ER methods in computational efficiency and real-time processing for on-demand tasks while ensuring reliability. We make FastER publicly available at: https://anonymous.4open.science/r/On_Demand_Entity_Resolution-9DFB